1. Field of the Invention
A method for estimating the hydraulic conductivity of a fracture zone in the sidewall of a borehole by use of transmitted and reflected Stoneley waves propagating in the annulus between an acoustic logging tool and the borehole sidewall.
2. Discussion of Related Art
Boreholes may be drilled the earth for the purpose of exploiting buried natural resources. Solid, water-soluble minerals such as certain sodium and potassium salts are mined by injecting water, dissolving the material and pumping the resulting brine to the surface. Non-soluble material such as sulphur may be melted using hot water and then pumped to the surface for processing. Fluidic resources such as steam, water, oil or gas usually migrate naturally into the well bore whence a desired fluid phase may be pumped to the surface for storage and distribution. Scavenging of hydrocarbon fluids by water injection may be used sometimes in the presence of a depleted reservoir formation.
The radial fluid migration from a homogeneous formation into the wellbore, or the reverse, is a function of the formation porosity, .phi., measured in percent, the permeability, .kappa., measured in darcies (m.sup.2, a measure of the inter-pore communication), the fluid viscosity, .mu. in Pascal-seconds (Pa.s), the pressure difference .DELTA.p in pascals (Pa) between the formation pore pressure and the hydrostatic pressure in the wellbore fluid and the vertical extent (thickness, H) of the zone of interest. As will be seen later, the critical parameter with respect to volumetric flow is hydraulic conductivity, Q, where Q=(.kappa..sub.0 H/.mu.).DELTA.p.
Formation fracture zones that intersect the borehole sidewall provide very significant conduits for radial fluid-flow intercommunication between the formation and the well bore. An open fracture increases the effective area exposed to the sidewall of the borehole thereby to increase the fluid interchange aperture between formation and borehole.
Fracturing associated with a reservoir containing a desired fluid enhances the volumetric recovery rate of the fluid. On the other hand, in an open hole through a barren formation, a fracture zone may result in serious leakage from the borehole into the formation, of the product being pumped up the borehole. In either case, it is useful to know the location and fluid-conducting capability of a fracture zone so that appropriate steps may be taken either to exploit the presence of the fracture zone to enhance product recovery or to seal off the fracture zone to reduce product loss.
The composition and texture of the borehole rocks are measured using an instrumented logging sonde that is lowered into the wellbore on the end of a cable. The data gathered by the downhole instruments are transmitted via suitable communication channels in the cable to data-processing and data-storage devices on the surface. Exemplary logging tools include, but are not limited to, borehole televiewers, induction loggers, resistivity logs, self-potential logs, gamma ray logs, neutron logs, velocity logs and various forms of acoustic loggers.
Acoustic logging methods may include use of compressional waves, shear waves, flexural waves and tube or Stoneley waves. In the study of formation fracture zones that intersect the borehole sidewall, use of Stoneley waves is preferred. As is well known, Stoneley waves are a guided wave that propagate along a fluid-solid interface such as the interface between the borehole drilling fluids and the borehole sidewall. Because they are guided waves, Stoneley waves do not suffer spherical spreading. Those waveforms are readily separated from other acoustic propagation modes on the basis of slowness, frequency and amplitude.
A typical acoustic logging tool, shown suspended in a borehole 8 in FIG. 1, consists of a mandrel 10 upon which are mounted an acoustic source 12 such as a piezo-electric mono-polar driver transducer and an array 15 including a plurality such as eight or more, monopolar receiver transducers, the first and last or which are designated as 14 and 14'. For brevity, these devices will be referred to simply as transmitter and receivers. The receivers are distributed along the length of the mandrel 10 at spaced-apart intervals such as 0.5 foot, with the lowest receiver 14 about 10 feet above source 12. Usually the lowest receiver 14 is midway between the ends 16 and 18 of mandrel 10. The mandrel includes instrumentation 17 for triggering source 12 at desired intervals, for partially processing the data downhole and for transmitting partially-processed data to the surface equipment such as control electronics 19, a programmed computer 20 and means 21 for displaying a multitrace log of borehole parameters.
Command and control signals from the surface equipment 20 are multiplexed down a cable 22 and data are returned up the cable to the surface equipment in response thereto. A standard logging cable such as 22 includes 7 conductors, a stress member and is suitably armored. Cable 22 supports mandrel 10 from a draw works 24 associated with surface equipment such as 19-21 which is electrically connected thereto by line 25. An odometer (not shown) associated with cable-guidance sheave 26, which is suspended from derrick 11, provides depth measurements for the sonde 10. Control and data signals may be transmitted in analog or digital format, but preferably digital. Caliper arms 36 and 36' provide measurements of the borehole radius as a function of depth.
In operation, the sonde 10 is preferably lowered into the borehole 8. Data are recorded as the tool is withdrawn upwards at a rate of about 0.5 ft/s or 1800 ft/hr. The source radiates an acoustic pulse preferably once per second (s). The center frequency of the pulse is customarily one kilohertz (kHz) by way of example but not by way of limitation. The flight time of a pulse from the source to the most remote receiver is but a few milliseconds (ms) so that doppler distortion of the waveforms due to upward motion will be minimal.
Fracture zones in formation 28 are shown at 30. A washout 32, to be discussed later, is shown associated with fracture 30. For purposes of this disclosure, a fracture zone may be analogous to a permeable stratum sandwiched between two impermeable strata. Drilling fluid usually fills the annulus 34 between the borehole sidewall and the sonde.
Certain acoustic properties of a fracture zone are not the same as the acoustic attributes of the competent formation above and below the fracture zone. As before stated, a Stoneley wave is a guided wave whose characteristics are controlled by the fluid-solid interface in the borehole. Stonely waves are not subject to inverse square spreading. For that reason, Stoneley waves are preferred for fracture-zone studies. A fracture zone not only provides an impedance discontinuity which gives rise to reflections but it also attenuates Stoneley waves transmitted across the zone.
U.S. Pat. No. 4,831,600, issued May 16, 1989 to Brian E. Hornby et al., entitled Borehole Logging Method for Fracture Detection and Evaluation, teaches a method for locating fractures in a subsurface formation by generating first signals representative of Stoneley waves from an acoustic source located on a logging tool in the borehole. A second signal is generated by an array of detectors that is representative of Stoneley waves propagating from the source that have been reflected from a fracture zone. The second signal is deconvolved with the first signal such that the time and magnitude of the peak envelope of the deconvolved signal provides an indication of the presence of the fracture zone. The magnitude of the deconvolved signal is a measure of the reflectivity of the fracture zone. Using an iterative solution for a range of widths, w, an estimated fracture-zone reflectivity is computed from the Stoneley wave frequency, Stoneley wave slowness, borehole radius and fluid viscosity. The width corresponding to the closest match of the observed and the estimated reflectivity is indicative of the fracture width.
U.S. Pat. 4,870,627, issued Sep. 26, 1989 to Kai Hsu et al., describes a Method and Apparatus or Detecting and Evaluating Borehole wall fractures. A borehole is penetrated by a logging tool that generates acoustic pulses and produces different receiver waveforms that are representative of acoustic waves passed through a common interval alongside the tool. From the waveforms there are selected late-arriving fracture-sensitive portions of the waveforms. From individual ones of said portions, values of a parameter are selected, such as Stoneley wave energy, that is representative of the sensitivity of respective portions of the waveform to a fracture in the borehole wall. The values of the parameter as a function of depth are compared to a threshold value. A fracture is identified within a particular depth interval when the comparisons made with the waveform portions attributable to different receivers and for a common depth in the depth interval are within a predetermined range.
Another method is taught by U.S. Pat. 4,888,740, issued Dec. 19, 1989 to Alain Brie et al., entitled Differential Energy Acoustic Measurements of a Formation Characteristic. This method acoustically investigates characteristics, such as fractures, of a borehole that penetrates a formation by taking differential Stoneley wave acoustic energy measurements between pairs of receivers of an array of receivers carried by the logging tool. The receivers all have the same spacing. The energy is that detected by the receivers in response to acoustic pulses generated by a transmitter spaced from the receivers on the tool. The differential energy measurements are stacked to obtain a differential stacked energy log.
The prior-art methods do not provide a reliable estimation of the fluid transport properties of a fracture zone for two reasons: First, previous models proposed assume planar boundaries at the top and bottom surfaces of the fracture and a uniform aperture. That assumption is not necessarily appropriate for describing borehole fractures with porous, tortuous conduits. Second, borehole fractures are often found associated with enlarged borehole segments, commonly referred to as washouts, which are formed while drilling through weakened, friable regions on pre-existing fracture zones. The effects of washouts are not properly compensated.
In a paper entitled Borehole Stoneley Wave Propagation Across Permeable Structures, published in Geophysical Prospecting, v. 41, pp 165-187, 1993, X. M. Tang et al., unlike classical authorities, teach that fracture permeability or hydraulic conductivity are the appropriate parameters to characterize fluid transport capabilities of fractures. The hydraulic conductivity is defined as integrated fluid mobility, that is, the ratio of permeability to viscosity over a selected zone of thickness H or (.kappa..sub.0 /.mu.) H. In the paper, the authors presented a simplified theory to account for Stoneley wave propagation across a fracture zone on the basis of one-dimensional forward modeling.
It is a purpose of this disclosure to formulate an inversion problem, based on a forward model, that may be solved from field-data measurements to evaluate the location and fluid-conducting capability of fracture zones and thin-bed permeable strata.